MULTI VAGUE HOMOMORPHISM

This paper introduces the concept of Multi vague homomorphism between Multi vague groups, where each element is characterized by a k- dimensional vector of truth and falsity membership values. The study extends classical group homomorphisms to settings with layered uncertainty by incorporating Multi dimensional vagueness. We establish key structural properties of Multi vague homomorphism and examine their behaviour on Multi vague normal groups. Further, the notion of Multi vague order of an element under such homomorphisms is defined and investigated. Several results are proved that demonstrate how these mappings preserve algebraic and membership structure. The findings generalize existing fuzzy and vague group theories and offer a more expressive framework for modeling algebraic systems under multiple levels of uncertainty